...arguments must ultimately be backed by greater correctness...

I'd certainly like to think so! I'm just suspicious of that intuition, especially in myself. The subjective impression that reasoning is for truth-seeking could be because it is. However, if it's not, as the lead article suggests, then we'd still be under the impression that our reasoning is in pursuit of truth and that those who disagree with us are willfully ignoring the truth. So we can't use that intuition as a guide to tell us about what's the case in this situation.

It's also worth noting that people generally aren't convinced by true arguments. They're usually convinced instead by peer pressure and repetition. Presenting a really crushing (!) argument that leaves no logical wiggle room left over can actually make the person who initially disagreed become more certain of their initial position and become resentful toward you. That really makes no sense if reason is supposed to be for truth-pursuit - but it makes a lot of sense if arguments are more about dominance than determining what's real.